Pith Number

pith:ISHHOTOD

pith:2026:ISHHOTODK574XI33SKBWF2UCLO

not attested not anchored not stored refs pending

The brachistochrone problem for a constant velocity traveler in static and spherically symmetric spacetimes

Junji Jia, Longfei Wang

arxiv:2607.29265 v1 · 2026-07-31 · gr-qc

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ISHHOTODK574XI33SKBWF2UCLO}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-08-03T01:23:04.032777Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

448e774dc3577fcba37b928362ea825b93143c34283180f46c19826c76686584

Aliases

arxiv: 2607.29265 · arxiv_version: 2607.29265v1 · doi: 10.48550/arxiv.2607.29265 · pith_short_12: ISHHOTODK574 · pith_short_16: ISHHOTODK574XI33 · pith_short_8: ISHHOTOD

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ISHHOTODK574XI33SKBWF2UCLO \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 448e774dc3577fcba37b928362ea825b93143c34283180f46c19826c76686584

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "69f267903271eb6ac91f5de9e33f65a8635e19d5bfb130e6ed417809535c2303",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-07-31T10:37:06Z",
    "title_canon_sha256": "20e5f190cc97aad50bf9f8e3cef332f5d33e259575117a676b1d5b55f99257cf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.29265",
    "kind": "arxiv",
    "version": 1
  }
}